Sparse Function-On-Scalar Regression Using a Group Bridge Approach with Application to IEEG Data

• Activity Number: 187 - Contributed Poster Presentations: Section on Nonparametric Statistics
• Type: Contributed
• Date/Time: Monday, July 29, 2019 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Zhengjia Wang* and John Magnotti and Michael Beauchamp and Meng Li
• Companies: Rice University and Baylor College of Medicine and Baylor College of Medicine and Rice University
• Keywords: Sparse functional regression; Functional group bridge; Iterative lasso; ADMM; B-Spline; Intracranial electroencephalography (iEEG)

Abstract

There is a surge of interest in functional data analysis to incorporate shape constraints into the regression functions tailored for specific applications with enhanced interpretability. One such example is sparse function that arises frequently in neuroscience where interpretable signals often are zero in most regions and non-zero in some local regions. In this paper, we consider the function-on-scalar setting and propose to model sparse regression coefficient functions using a group bridge approach to capture both global and local sparsity. We use B-splines to transform sparsity of coefficient functions to its sparse vector counterpart of increasing dimension. We propose a non-convex optimization algorithm to solve the involved penalized least square error loss function, with theoretically guaranteed numerical convergence and scalable implementation. Some asymptotic properties are provided. We illustrate the proposed method through simulation and an application to an intracranial electroencephalography (iEEG) dataset.